Full Description
Statistics is made simple with this award-winning guide to using R and applied statistical methods.
With a clear step-by-step approach explained using real world examples, learn the practical skills you need to use statistical methods in your research from an expert with over 30 years of teaching experience. With a wealth of hands-on exercises and online resources created by the author, practice your skills using the data sets and R scripts from the book with detailed screencasts that accompany each script.
This book is ideal for anyone looking to:
• Complete an introductory course in statistics
• Prepare for more advanced statistical courses
• Gain the transferable analytical skills needed to interpret research from across the social sciences
• Learn the technical skills needed to present data visually
• Acquire a basic competence in the use of R and RStudio.
This edition also includes a gentle introduction to Bayesian methods integrated throughout.
The author has created a wide range of online resources, including: over 90 R scripts, 36 datasets, 37 screen casts, complete solutions for all exercises, and 130 multiple-choice questions to test your knowledge.
Contents
Chapter 1: Introduction and R Instructions
Basic Terminology
Data: Qualitative or Quantitative
Data: Cross-Sectional or Longitudinal
Descriptive Statistics
Probability
Statistics: Estimation and Inference
Chapter 2: Descriptive Statistics: Tabular and Graphical Methods
Methods of Summarizing and Displaying Qualitative Data
Methods of Summarizing and Displaying Quantitative Data
Cross Tabulations and Scatter Plots
Chapter 3: Descriptive Statistics: Numerical Methods
Measures of Central Tendency
Measures of Location
Exploratory Data Analysis: The Box Plot Display
Measures of Variability
The z-Score: A Measure of Relative Location
Measures of Association: The Bivariate Case
The Geometric Mean
Chapter 4: Introduction to Probability
Some Important Definitions
Counting Rules
Assigning Probabilities
Events and Probabilities
Probabilities of Unions and Intersections of Events
Conditional Probability
Bayes' Theorem and Events
Chapter 5: Discrete Probability Distributions
The Discrete Uniform Probability Distribution
The Expected Value and Standard Deviation of a Discrete Random Variable
The Binomial Probability Distribution
The Poisson Probability Distribution
The Hypergeometric Probability Distribution
The Hypergeometric Probability Distribution: The General Case
Bayes' Theorem and Discrete Random Variables
Chapter 6: Continuous Probability Distributions
Continuous Uniform Probability Distribution
Normal Probability Distribution
Exponential Probability Distribution
Optional Material: Derivation of the Cumulative Exponential Probability Func- tion
Bayes' Theorem and Continuous Random Variables
Chapter 7: Point Estimation and Sampling Distributions
Populations and Samples
The Simple Random Sample
The Sample Statistic: x, s, and p
The Sampling Distribution of x
The Sampling Distribution of p
Some Other Commonly Used Sampling Methods
Bayes' Theorem: Approximate Bayesian Computation
Chapter 8: Confidence Interval Estimation
Interval Estimate of µ When σ Is Known
Interval Estimate of µ When σ Is Unknown
Sample Size Determination in the Case of µ
Interval Estimate of p
Sample Size Determination in the Case of p
Bayes' Theorem: Confidence Intervals or Credible Intervals
Chapter 9: Hypothesis Tests: Introduction, Basic Concepts, and an Example
Chapter 10: Hypothesis Tests about Means and Proportions: Applications
The Lower-Tail Hypothesis Test about μ: σ Is Known
The Two-Tail Hypothesis Test about μ: σ Is Known
The Upper-Tail Hypothesis Test about μ: σ Is Unknown
The Two-Tail Hypothesis Test about μ: σ is Unknown
Hypothesis Tests about p
Calculating the Probability of a Type II Error: β
Adjusting the Sample Size to Control the Size of β
Bayes' Theorem and an Inferential Approach to p
Chapter 11: Comparisons of Means and Proportions
The Difference between μ1 and μ2: Independent Samples
The Difference between μ1 and μ2: Paired Samples
The Difference between p1 and p2: Independent Samples
Bayes' Theorem and the Difference between p1 and p2
Chapter 12: Simple Linear Regression
Simple Linear Regression: The Model
The Estimated Regression Equation
Goodness of Fit: The Coefficient of Determination, r2
The Hypothesis Test about β1
Alternative Approaches to Testing Significance
So Far, We Have Tested Only b1. Will We Also Test b0?
Assumptions: What Are They?
Assumptions: How Are They Validated?
Optional Material: Derivation of the Expressions for the Least-Squares Estimates of β0 and β1
Bayes' Theorem: Using Stan to Estimate the Relationship between Two Variables
Chapter 13: Multiple Regression
Simple Linear Regression: A Reprise
Multiple Regression: The Model
Multiple Regression: The Multiple Regression Equation
The Estimated Multiple Regression Equation
Multiple Regression: The 2 Independent Variable Case
Assumptions: What Are They? Can We Validate Them?
Tests of Significance: The Overall Regression Model
Tests of Signicance: The Independent Variables
There Must Be An Easier Way Than This, Right?
Using the Estimated Regression Equation for Prediction
Independent Variable Selection: The Best-Subsets Method
Logistic Regression: The Zero-One Dependent Variable
Bayes' Theorem: Stan and Multiple Regression Analysis
